Many clustering methods have been proposed for analyzing the relations inside networks with a mixture of assortative and disassortative structures. All these methods are based on the fact that the entire network is observable. However, the entities in some real networks may be private, and thus, cannot be observed. We focus on private peer-to-peer networks in which all vertices are independent and private, and each vertex only knows about itself and its neighbors. We propose a privacy-preserving Gibbs sampling for clustering these types of private networks and detecting their mixed structures without revealing any private information about any individual entity. Moreover, the running cost of our method is related only to the number of clusters and the maximum degree, but is nearly independent of the number of vertices in the entire network.
